Calibration of interest rate term structure and derivative pricing models
We argue interest rate derivative pricing models are misspecified so that when they are fitted to historical data they do not produce prices consistently with the market. Interest rate models have to be calibrated to prices to ensure consistency. There are few published works on calibration to derivatives prices and we make this the focus of our thesis. We show how short rate models can be calibrated to derivatives prices accurately with a second time dependent parameter. We analyse the misspecification of the fitted models and their implications for other models. We examine the Duffle and Kan Affine Yield Model, a class of short rate models, that appears to allow easier calibration. We show that, in fact, a direct calibration of Duffle and Kan Affine Yield Models is exceedingly difficult. We show the non-negative subclass is equivalent to generalised Cox, Ingersoll and Ross models that facilitate an indirect calibration of nonnegative Duffle and Kan Affine Yield Models. We examine calibration of Heath, Jarrow and Morton models. We show, using some experiments, Heath, Jarrow and Morton models cannot be calibrated quickly to be of practical use unless we restrict to special subclasses. We introduce the Martingale Variance Technique for improving the accuracy of Monte Carlo simulations. We examine calibration of Gaussian Heath Jarrow and Morton models. We provide a new non-parametric calibration using the Gaussian Random Field Model of Kennedy as an intermediate step. We derive new approximate swaption pricing formulae for the calibration. We examine how to price resettable caps and floors with the market- Libor model. We derive a new relationship between resettable caplets and floorlets prices. We provide accurate approximations for the prices. We provide practical approximations to price resettable caplets and floorlets directly from quotes on standard caps and floors. We examine how to calibrate the market-Libor model.